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A uniquely Hamiltonian graph is a graph possessing a single Hamiltonian cycle. Classes of uniquely Hamiltonian graphs include the cycle graphs C_n, Hanoi graphs H_n, ladder ...

A zero-symmetric graph is a vertex-transitive cubic graph whose edges are partitioned into three orbits by its automorphism group. The figures above show some small ...

The Van Lint-Schrijver Graph graph is a weakly regular Hamiltonian graph on 162 vertices with parameters (nu,k,lambda,mu)=(162,(6),(0),(0,1)). It is distance-regular with ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

The Hochberg-O'Donnell fish graph is the unit-distance graph on 23 nodes and 42 edges illustrated above. It is triangle-free and is the smallest example of a unit-distance ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

Tutte's (46-vertex) graph is a cubic nonhamiltonian graph contructed by Tutte (1946) as a counterexample to Tait's Hamiltonian graph conjecture by using three copies ...

A maze, also known as a labyrinth, as is a set of passages (with impermeable walls). The goal of the maze is to start at one given point and find a path through the passages ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...